23.4.95 problem 95

Internal problem ID [6397]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 4. THE NONLINEAR EQUATION OF SECOND ORDER, page 380
Problem number : 95
Date solved : Tuesday, September 30, 2025 at 02:56:15 PM
CAS classification : [NONE]

\begin{align*} \left (1+a \right ) x y^{\prime }+x^{2} y^{\prime \prime }&=x^{k} f \left (x^{k} y, k y+x y^{\prime }\right ) \end{align*}

✗ Maple

ode:=(a+1)*x*diff(y(x),x)+x^2*diff(diff(y(x),x),x) = x^k*f(x^k*y(x),k*y(x)+x*diff(y(x),x)); 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(1 + a)*x*D[y[x],x] + x^2*D[y[x],{x,2}] == x^k*f[x^k*y[x], k*y[x] + x*D[y[x],x]]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
a = symbols("a") 
k = symbols("k") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + x*(a + 1)*Derivative(y(x), x) - x**k*f(x**k*y(x), k*y(x) + x*Derivative(y(x), x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : multiple generators [_X0, f(x**k*y(x), _X0*x + k*y(x))] 
No algorithms are impl